Self-contained sequels are allowed.

The two that leap immediately to mind that are available on PS3, since that's what you said you own, are Heavy Rain and Bioshock.  Both single player games, both amazing, and both unique experiences totally unlike any other game you could play.  Bonus points for both since they have been out for a long time which means you can get them relatively cheap, which is good since you said money is an issue. 

If you have access to a 360, I would highly recommend Fable 2, even if you have never played the first one.  It is absolutely brilliant and beautiful, and once again has the added bonus of being cheap to purchase.

Also, it's old, but you can get Knights of the Old Republic (PC) on Steam for $10, and I would be hard-pressed to think of a better, more engaging game you can get for that price.  Also it will run on pretty much any PC.

Deus Ex sometimes is like 3.00 on steam. And it's tied (With 5 others for my favorite game)


New Single Player Games I've Played (My Rating)
The Legend of Heroes: Trails in the Sky (9.5)
Bioshock (9) (Sorta a sequal, to system shock... except it's not)
Metro 2033 (9)



But for me Ones I will Play

Fragile Dreams (Wii)  (Bought this yet to play it)
Xenoblade Chronicles (Wii)
Last Story Wii (Wii)
Rage (PC)

WTF I've boughten 1 wii game ever! (rented others) and suddenly theres 2 when everyone says the wii is dieing.

and Boom goes the dynamite. Highlighted all the gaes I think are really important.

Also I would like to add

Mass Effect (and Mass Effect 2)

Gears of War (and Gears 2)

Valkeria Chronicles

Folklore

Metroid Prime 3: Corruption

Vanquish

Assassin's Creed (Play all of them)

Lost Planet 1

Dead Rising

Fallout 3 (not really related to prior installments)

Project Sylpheed (bad ratings for being short, but a damn good $5, 5 hour game)

Dead Space

The Legend of Zelda: Twilight Princess (weak overarching story)

Super Mario Galaxy (1 & 2)

Mario Kart Wii

Forza Motorsport 2 and 3

GT5

Project Gotham Racing 3 and 4

Blur

Need for Speeds

Burnout

Call of Duty 2, 4, MW2

Too Human

etc.

Bolded games are the big ones

Super Mario Galaxy

Little Big Planet

Little King's Story

Rune Factory Frontier

Okami

Bioshock

S.T.A.L.K.E.R. - Great FPS with RPG and exploration elements

Bioshock - FPS with great atmosphere

Magica - inovative indie action adventure/top down shooter game

X-Com/UFO: Enemy unknown - the best squad based turn based tactical game around 

Batman: AA -great action adventure game and a must for all batman fans

Mount & Blade - best open ended medevil war simulator RPG ever

Alpha Centauri - the best non sequel Civ game ; )

Knights of the old republic - a must for any Star wars fan

The Witcher - one of the best uses of morality in a modern RPG

Portal - it's one hell of a special first person puzzle adventure

Minecraft - An open ended mining/building/adventure sim

Prince of Persia: the sands of time - still one of the best 3D action adventures ever made

Dead Space - 3rd person shooter horor game 

and that is all i can think of at the moment

Do you rule out new installments of sports titles?

Oh man. I love these posts. /thread

I didn't realize you didn't own a Wii. In that case here are some recommendations for PC:

• Beyond Good & Evil - definitely a  "must play". It's a 3D free-roaming Zelda like adventure by Michael Ancel, the man behind the original Rayman games. Features a unique world and cool cartoon sci-fi setting. Probably cheap on steam too, since this game is the definition of underrated (game sold terribly even when originally released...)
• Abe's Odyssey - this is a 2D side scrolling adventure originally released during the playstation era but the style and amazing art design make it a classic. Along with its sequel - Abe's Exodus - it can also be bought on steam for cheap. The two later games in the series, which were originally released on XBOX and are full 3D, are also coming to steam with at least one of them receiving a graphical update. Anybody who calls themselves a gamer should experience these beautiful games.
• The Elder Scrolls 3: Morrowind - the first fully 3D elder scrolls game, considered by most to be much better than Oblivion. The benefit of playing on PC is that modders have released graphical updates for nearly every aspect of the game so you can still get some "bang" out of your new PC if you play this one. Together with its two expansions - Tribunal and Bloodmoon (which lets you play the whole game as a werewolf) - there are literally hundreds of hours of single-player content here.
• If you are done with these and still have an appetite for epic single player games, by all means play
  The Longest Journey as it has a brilliant story and is also a true classic.
• Another classic in the same genre as TLS (point and click adventure) that should not be missed is
  Grim Fandango, which has you play a skeleton journeying through the Mexican land of the dead in a film-noir setting the likes of which hasn't been seen before or since. Yet another work of art, as far as games are concerned.

That's it for now. I could go on forever really, but these games should keep you busy for a long time and every single one of them is a masterpiece.